document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=655216>Question 655216</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Construct a scatterplot for the (x, y) values below, and answer the following questions.  You needn’t submit your scatterplot with your answer.\r<BR>\n" );
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document.write( "x	y<BR>\n" );
document.write( "1	4<BR>\n" );
document.write( "2	6<BR>\n" );
document.write( "3	8<BR>\n" );
document.write( "4	10<BR>\n" );
document.write( "5	11\r<BR>\n" );
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document.write( "- Based on the scatterplot, would the correlation between x and y be positive or negative?\r<BR>\n" );
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document.write( "-  How would you interpret these data in terms of linear regression? Please be sure to see the model in problem 6 of practice items posted in the P&S area\r<BR>\n" );
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document.write( "Could you please show work <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #408995 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=408995\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "x | y<BR>\n" );
document.write( "1 | 4<BR>\n" );
document.write( "2 | 6<BR>\n" );
document.write( "3 | 8<BR>\n" );
document.write( "4 | 10<BR>\n" );
document.write( "5 | 11\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope%28m%29=+%28y2-y1%29%2F%28x2-x1%29 ALIGN=MIDDLE  ALT=\"slope%28m%29=+%28y2-y1%29%2F%28x2-x1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.... find the slope\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=slope%28m%29=%286-4%29%2F%282-1%29=+3%2F1=3 ALIGN=MIDDLE  ALT=\"slope%28m%29=%286-4%29%2F%282-1%29=+3%2F1=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "find the equation:\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=find_line_by_slope_and_point.solver>FIND a line by slope and one point</A></TD></TR>\n" );
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document.write( "  What we know about the line whose equation we are trying to find out:<BR>\n" );
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document.write( "      <LI>it goes through point (1, 4)</LI><BR>\n" );
document.write( "      <LI>it has a slope of 3</LI><BR>\n" );
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document.write( "  First, let's draw a diagram of the coordinate system with point (1, 4) plotted with a little blue dot:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A++++drawing%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0A+++++++++++++grid%281%29%2C%0D%0A+++++++++++++blue%28+circle%28+1%2C+4%2C+0.2+%29+%29+%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "    <B>Write this down</B>: the formula for the equation, given point <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D%2C+y%5B1%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D%2C+y%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and intercept a, is<BR>\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ax+%2B+%28y%5B1%5D-a%2Ax%5B1%5D%29 ALIGN=MIDDLE  ALT=\"y=ax+%2B+%28y%5B1%5D-a%2Ax%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (see a paragraph below explaining why this formula is correct)<BR>\n" );
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document.write( "    Given that a=3, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x%5B1%5D+=+1%2C+y%5B1%5D+=+4+%29+ ALIGN=MIDDLE  ALT=\"system%28+x%5B1%5D+=+1%2C+y%5B1%5D+=+4+%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have the equation of the line:<BR>\n" );
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document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3%2Ax+%2B+1 ALIGN=MIDDLE  ALT=\"y=3%2Ax+%2B+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "    Explanation: <I>Why did we use formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=ax+%2B+%28y%5B1%5D+-+a%2Ax%5B1%5D%29 ALIGN=MIDDLE  ALT=\"y=ax+%2B+%28y%5B1%5D+-+a%2Ax%5B1%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ? Explanation goes here. We are trying to find equation y=ax+b. The value of slope (a) is already given to us. We need to find b. If a point (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D ALIGN=MIDDLE  ALT=\"y%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >) lies on the line, it means that it satisfies the equation of the line. So, our equation holds for (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D ALIGN=MIDDLE  ALT=\"y%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >): <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D+=+a%2Ax%5B1%5D%2Bb ALIGN=MIDDLE  ALT=\"y%5B1%5D+=+a%2Ax%5B1%5D%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" > Here, we know a, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5B1%5D ALIGN=MIDDLE  ALT=\"y%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and do not know b. It is easy to find out: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=y%5B1%5D-a%2Ax%5B1%5D ALIGN=MIDDLE  ALT=\"b=y%5B1%5D-a%2Ax%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So, then, the equation of the line is: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+y=ax%2B%28y%5B1%5D-a%2Ax%5B1%5D%29+ ALIGN=MIDDLE  ALT=\"+y=ax%2B%28y%5B1%5D-a%2Ax%5B1%5D%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >. </I><BR>\n" );
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document.write( "    Here's the graph:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%0D%0A++++drawing%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C%0D%0A+++++++++++++grid%281%29%2C%0D%0A+++++++++++++graph%28+400%2C+400%2C+-10%2C+10%2C+-10%2C+10%2C+3%2Ax%2B1+%29%2C%0D%0A+++++++++++++blue%28+circle%28+1%2C+4%2C+0.2+%29+%29%2C%0D%0A+++++++++++++locate%28+1%2C+4%2C+%22%281%2C+4%29%22+%29+%29%0D%0A+++++++++++++%29%0D%0A++++++++++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Correlation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=positive ALIGN=MIDDLE  ALT=\"positive\"   DISABLED_style= \"max-width:90%; height:auto;\" > since as x rises, y rises\r<BR>\n" );
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